```
class Solution {
public:
int getMoneyAmount(int n) {
vector<vector<int>> dp(n + 2, vector<int>(n + 2));
for(int len = 2; len <= n; len++) { //iterate through the length of the interval start from 2 because if len == 1, we need to pay 0,
for(int i = 1; i + len - 1 <= n; i++) {
int j = i + len - 1;
dp[i][j] = numeric_limits<int>::max();
for(int k = i; k <= j; k++) { //select a number k in [i, j]
dp[i][j] = min(dp[i][j], k + max(dp[i][k - 1], dp[k + 1][j]));
}
}
}
return dp[1][n];
}
};
```